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Find missing side lengths in perimeter problems

Perimeter is the total distance around a two-dimensional figure, so a missing side length can be found by subtracting the sum of the known side lengths from the given perimeter; in rectangles, opposite sides have equal lengths and can provide additional information. The reasoning connects labeled diagrams, addition, subtraction, units, and the distinction between perimeter and area, using whole-number measurements in familiar rectangles and simple polygons rather than algebraic expressions or fractional, decimal, or irregular cases.

Detailed Explanation: Find missing side lengths in perimeter problems

Perimeter is the total distance around a shape. To find a missing side:

  1. Add the lengths of all the known sides.
  2. Subtract that sum from the perimeter.
  3. Write the answer with the correct unit.

For a rectangle, opposite sides have equal lengths.

Example: A rectangle has a perimeter of 26 cm26\text{ cm}. Three sides are labeled 8 cm8\text{ cm}, 8 cm8\text{ cm}, and 5 cm5\text{ cm}. Find the missing side.

First, add the known side lengths:

8+8+5=21 cm8+8+5=21\text{ cm}

The known sides make up 21 cm21\text{ cm} of the perimeter. Subtract from the total perimeter:

26−21=5 cm26-21=5\text{ cm}

So, the missing side is 5 cm5\text{ cm}.

Check: The rectangle’s side lengths are 88, 55, 88, and 55.

8+5+8+5=26 cm8+5+8+5=26\text{ cm}

Remember, perimeter measures the distance around a shape. Area measures the space inside a shape.

Learn by doing: Find missing side lengths in perimeter problems

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    Perimeter of a Rectangle - Side from Perimeter and Side

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